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JEE Main Math Class 12 Three Dimensional Geometry Part 1 Questions
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© examsnet.com
Question : 16
Total: 100
A variable plane passes through a fixed point (3,2,1) and meets
x
,
y
and
z
axes at
A
,
B
and
C
respectively. A plane is drawn parallel to
y
z
−
plane through
A
,
a second plane is drawn parallel
z
x
−
plane through
B
and a third plane is drawn parallel to
x
y
−
plane through
C
. Then the locus of the point of intersection of these three planes, is
[Online April 15, 2018]
x
+
y
+
z
=
6
x
3
+
y
2
+
z
1
=
1
3
x
+
2
y
+
1
z
=
1
1
x
+
1
y
+
1
z
=
11
6
Validate
Solution:
If
a
,
b
,
c
are the intercepts of the variable plane on the
x
,
y
,
z
axes respectively, then the equation of the plane is
x
a
+
y
b
+
z
c
=
1
And the point of intersection of the planes parallel to the
x
y
,
y
z
and
z
x
planes is
(
a
,
b
,
c
)
.
As the point (3,2,1) lies on the variable plane, so
3
a
+
2
b
+
1
c
=
1
Therefore, the required locus is
3
x
+
2
y
+
1
z
=
1
© examsnet.com
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